What is the probability they sum to 9, 3, or 6?

Question

involving the sum of two die rolls.
(1) What is the probability they sum to 9, 3, or 6?

(2) What is the probability they sum to at least 7?

Answer 1

There are 36 possible outcomes when you roll two dice (6 on each die)

 

There are 4 ways to get a sum of 9: (3,6), (4,5), (5,4), or (6,3) so P(9) = 4/36

There are 2 ways to get a sum of 3: (1,2) or (2,1) so P(3) = 2/36

There are 5 ways to get a sum of 6: (1,5), (2,4), (3,3), (4,2) or (5,1) so P(6) = 5/36 

 

So P(sum = 9, 3, or 6) = 4/36 + 2/36 + 5/36 = 11/36 

 

To find the probability that the sum is at least 7 you need to figure out P(7), P(8), P(9), P(10), P(11) and P(12).  I won't enumerate them (although you should for practice) but the values are 

 

P(7)   = 6/36

P(8)   = 5/36

P(9)   = 4/36

P(10) = 3/36

P(11) = 2/36

P(12) = 1/36

 

Do you see the pattern?  So 

 

P(sum >=7) = 6/36 + 5/36 + 4/36 + 3/36 + 2/36 + 1/36 = 21/36 = 7/12